Nonlinear dynamics of taillight effect in mixed traffic flow driven by competing visual delay and V2X communication

This study investigates the impact of the taillight effect on the stability of mixed traffic flow. Constrained by physiological limitations, human drivers inevitably exhibit visual reaction delays when perceiving brake lights. Conversely, connected vehicles leverage V2X communication to receive electronic signals, enabling instantaneous feedback and beyond-visual-range perception. These distinct characteristics create a competitive relationship regarding their contributions to system stability. Thus, this study explicitly defines this competition by employing the connected vehicle penetration rate as a weighting parameter. By incorporating this into a lattice hydrodynamic model, we quantify the unique competitive mechanism between the lag of human visual perception and the instantaneity of V2X communication. Through linear stability analysis, we derive the critical stability criterion and reveal how the penetration rate of connected vehicles offsets the instability caused by human physiological delay. On this basis, we carry out nonlinear analysis using the reductive perturbation method to derive the modified mKdV equation near the critical point and obtain the analytical solution for the kink-antikink soliton. Numerical simulations confirm the theoretical predictions and demonstrate that increasing the penetration rate of connected vehicles significantly modifies the dispersion coefficient of traffic flow. These results substantiate that the competition mechanism under the taillight effect effectively eliminates the hysteresis loop and phantom jam caused by visual delay and enhances the robustness of the traffic system against the physiological limitations of human drivers.